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Gaussian Elimination Guide

The Gaussian elimination method reduces an augmented matrix, formed by placing a matrix of coefficients next to a vector of constants, into an upper triangular matrix using row transformations. The method then solves for the unknowns by backward substitution, starting with the last equation and substituting values into the previous equations. This produces a resulting upper triangular matrix with the coefficients on and above the diagonal and constants on the right, allowing the unknowns to be solved sequentially.

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62 views3 pages

Gaussian Elimination Guide

The Gaussian elimination method reduces an augmented matrix, formed by placing a matrix of coefficients next to a vector of constants, into an upper triangular matrix using row transformations. The method then solves for the unknowns by backward substitution, starting with the last equation and substituting values into the previous equations. This produces a resulting upper triangular matrix with the coefficients on and above the diagonal and constants on the right, allowing the unknowns to be solved sequentially.

Uploaded by

Lanz de la Cruz
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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GAUSS REDUCTION OR GAUSSIAN

ELIMINATION METHOD

PRINCIPLE:
TO REDUCE OR CONVERT THE
AUGMENTED MATRIX (A MATRIX
FORMED BY PLACING SIDE BY SIDE
TWO OR MORE MATRICES. AUGMENT
THE MATRIX OF COEFFICIENT WITH
THE VECTOR OF CONSTANTS.) INTO
AN UPPER DIAGONAL MATRIX BY ROW
TRANSFORMATION.
SOLVE FOR THE UNKNOWNS BY BACKWARD
SUBSTITUTION.

a11 x 1 a12 x 2 a13 x 3 b1


a21 x 1 a22 x 2 a23 x 3 b2
a31 x 1 a32 x 2 a33 x 3 b3
AUGMENTED MATRIX
a11 a12 a13 b1
a21 a22 a23 b2
a31 a32 a33 b3
RESULTING UPPER DIAGONAL MATRIX

A 11 A 12 A 13 B1
0 A 22 A 23 B2
B3 0 0 A 33 B3
x3
A 33
B2 A 23 x 3
x2
A 22
B1 A 13 x 3 A 12 x 2
x1
A 11

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